Phase II dose-response trials: A simulation study to compare analysis method performance under design considerations

Phase II trials are intended to provide information about the dose-response relationship and to support the choice of doses for a pivotal phase III trial. Recently, new analysis methods have been proposed to address these objectives, and guidance is needed to select the most appropriate analysis method in specific situations. We set up a simulation study to evaluate multiple performance measures of one traditional and three more recent dose-finding approaches under four design options and illustrate the investigated analysis methods with an example from clinical practice. Our results reveal no general recommendation for a particular analysis method across all design options and performance measures. However, we also demonstrate that the new analysis methods are worth the effort compared to the traditional ANOVA-based approach.

Model selection versus model averaging in dose finding studies

A key objective of Phase II dose finding studies in clinical drug development is to adequately characterize the dose response relationship of a new drug. An important decision is then on the choice of a suitable dose response function to support dose selection for the subsequent Phase III studies. In this paper, we compare different approaches for model selection and model averaging using mathematical properties as well as simulations. We review and illustrate asymptotic properties of model selection criteria and investigate their behavior when changing the sample size but keeping the effect size constant. In a simulation study, we investigate how the various approaches perform in realistically chosen settings. Finally, the different methods are illustrated with a recently conducted Phase II dose finding study in patients with chronic obstructive pulmonary disease. Copyright © 2016 John Wiley & Sons, Ltd.

Multiple comparison procedure and modeling: a versatile tool for evaluating dose-response relationships in veterinary pharmacology - a case study with furosemide

Congestive heart failure (CHF) is a leading cause of mortality with an increasing prevalence in human and canine populations. While furosemide is a loop diuretic prescribed for the majority of CHF patients to reduce fluid retention, it also activates the renin-angiotensin aldosterone system (RAAS) which further contributes to the accelerated progression of heart failure. Our objective was to quantify the effect of furosemide on diuresis, renin activity (RA), and aldosterone (AL) in dogs, using a combined multiple comparisons and model-based approach (MCP-Mod). Twenty-four healthy beagle dogs were allocated to four treatment groups (saline vs. furosemide 1, 2, and 4 mg/kg i.m., q12 h for 5 days). Data from RA and AL values at furosemide trough concentrations, as well as 24-h Diuresis, were analyzed using the MCP-Mod procedure. A combination of E_max models adequately described the dose-response relationships of furosemide for the various endpoints. The dose-response curves of RA and AL were found to be well in agreement, with an apparent shallower slope compared with 24-h Diuresis. The research presented herein constitutes the first application of MCP-Mod in Veterinary Medicine. Our data show that furosemide produces a submaximal effect on diuresis at doses lower than those identified to activate the circulating RAAS.

Viewpoint: model selection uncertainty, pre-specification, and model averaging

Scientific progress in all empirical sciences relies on selecting models and performing inferences from selected models. Standard statistical properties (e.g., repeated sampling coverage probability of confidence intervals) cannot be guaranteed after a model selection. This viewpoint reviews this dilemma, puts the role that pre-specification can play into perspective and illustrates model averaging as a way to relax the problem of model selection uncertainty.

Practical considerations for using functional uniform prior distributions for dose-response estimation in clinical trials

Estimating nonlinear dose-response relationships in the context of pharmaceutical clinical trials is often a challenging problem. The data in these trials are typically variable and sparse, making this a hard inference problem, despite sometimes seemingly large sample sizes. Maximum likelihood estimates often fail to exist in these situations, while for Bayesian methods, prior selection becomes a delicate issue when no carefully elicited prior is available, as the posterior distribution will often be sensitive to the priors chosen. This article provides guidance on the usage of functional uniform prior distributions in these situations. The essential idea of functional uniform priors is to employ a distribution that weights the functional shapes of the nonlinear regression function equally. By doing so one obtains a distribution that exhaustively and uniformly covers the underlying potential shapes of the nonlinear function. On the parameter scale these priors will often result in quite nonuniform prior distributions. This paper gives hints on how to implement these priors in practice and illustrates them in realistic trial examples in the context of Phase II dose-response trials as well as Phase I first-in-human studies.

Unimodal regression using Bernstein-Schoenberg splines and penalties

Research in the field of nonparametric shape constrained regression has been intensive. However, only few publications explicitly deal with unimodality although there is need for such methods in applications, for example, in dose-response analysis. In this article, we propose unimodal spline regression methods that make use of Bernstein-Schoenberg splines and their shape preservation property. To achieve unimodal and smooth solutions we use penalized splines, and extend the penalized spline approach toward penalizing against general parametric functions, instead of using just difference penalties. For tuning parameter selection under a unimodality constraint a restricted maximum likelihood and an alternative Bayesian approach for unimodal regression are developed. We compare the proposed methodologies to other common approaches in a simulation study and apply it to a dose-response data set. All results suggest that the unimodality constraint or the combination of unimodality and a penalty can substantially improve estimation of the functional relationship.

Functional uniform priors for nonlinear modeling

This article considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function. Using results on how to construct uniform distributions in general metric spaces, we propose a prior distribution that is uniform in the space of functional shapes of the underlying nonlinear function and then back-transform to obtain a prior distribution for the original model parameters. The primary application considered in this article is nonlinear regression, but the idea might be of interest beyond this case. For nonlinear regression the so constructed priors have the advantage that they are parametrization invariant and do not violate the likelihood principle, as opposed to uniform distributions on the parameters or the Jeffrey's prior, respectively. The utility of the proposed priors is demonstrated in the context of design and analysis of nonlinear regression modeling in clinical dose-finding trials, through a real data example and simulation.

Stochastically ordered multiple regression

In various application areas, prior information is available about the direction of the effects of multiple predictors on the conditional response distribution. For example, in epidemiology studies of potentially adverse exposures and continuous health responses, one can typically assume a priori that increasing the level of an exposure does not lead to an improvement in the health response. Such an assumption can be formalized through a stochastic ordering assumption in each of the exposures, leading to a potentially large improvement in efficiency in nonparametric modeling of the conditional response distribution. This article proposes a Bayesian nonparametric approach to this problem based on characterizing the conditional response density as a Gaussian mixture, with the locations of the Gaussian means varying flexibly with predictors subject to minimal constraints to ensure stochastic ordering. Theoretical properties are considered and Markov chain Monte Carlo methods are developed for posterior computation. The methods are illustrated using simulation examples and a reproductive epidemiology application.